{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LZ5N3ELKSJANP62V43PB5T7Z6Y","short_pith_number":"pith:LZ5N3ELK","schema_version":"1.0","canonical_sha256":"5e7add916a9240d7fb55e6de1ecff9f634405ddcb424c142e63c08e95091e3a0","source":{"kind":"arxiv","id":"1401.5748","version":1},"attestation_state":"computed","paper":{"title":"KAM-tori near an analytic elliptic fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Fayad, H. Eliasson, R. Krikorian","submitted_at":"2014-01-22T18:25:54Z","abstract_excerpt":"We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $\\o_0$ is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\\\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that $\\o_0$ has rationally independent coo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.5748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-22T18:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"f04891c6d511e8bb4a69456c750f32b80af3a4940cb2e605098c4d110d36678f","abstract_canon_sha256":"2330fd1467230d45fa90d9c00d37b17c579b559fe1b9ccb5a9a703fff1c3b8e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:24.775987Z","signature_b64":"1OWjpdy08XQzZNMfc2/XNVKeKDBAuQJHWZ15c6uY0TILX9d2SGffeQn+CktcldJMfN8KR97T2c3OdWz1d+xfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e7add916a9240d7fb55e6de1ecff9f634405ddcb424c142e63c08e95091e3a0","last_reissued_at":"2026-05-18T03:01:24.775400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:24.775400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"KAM-tori near an analytic elliptic fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Fayad, H. Eliasson, R. Krikorian","submitted_at":"2014-01-22T18:25:54Z","abstract_excerpt":"We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $\\o_0$ is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\\\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that $\\o_0$ has rationally independent coo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5748","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.5748","created_at":"2026-05-18T03:01:24.775495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.5748v1","created_at":"2026-05-18T03:01:24.775495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5748","created_at":"2026-05-18T03:01:24.775495+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZ5N3ELKSJAN","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZ5N3ELKSJANP62V","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZ5N3ELK","created_at":"2026-05-18T12:28:38.356838+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y","json":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y.json","graph_json":"https://pith.science/api/pith-number/LZ5N3ELKSJANP62V43PB5T7Z6Y/graph.json","events_json":"https://pith.science/api/pith-number/LZ5N3ELKSJANP62V43PB5T7Z6Y/events.json","paper":"https://pith.science/paper/LZ5N3ELK"},"agent_actions":{"view_html":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y","download_json":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y.json","view_paper":"https://pith.science/paper/LZ5N3ELK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.5748&json=true","fetch_graph":"https://pith.science/api/pith-number/LZ5N3ELKSJANP62V43PB5T7Z6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/LZ5N3ELKSJANP62V43PB5T7Z6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y/action/storage_attestation","attest_author":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y/action/author_attestation","sign_citation":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y/action/citation_signature","submit_replication":"https://pith.science/pith/LZ5N3ELKSJANP62V43PB5T7Z6Y/action/replication_record"}},"created_at":"2026-05-18T03:01:24.775495+00:00","updated_at":"2026-05-18T03:01:24.775495+00:00"}